Carol would like to become an Olympic sprinter. Her younger sister Jane would rather play football, but helps Carol by racing against her. When they tried the 100 metre dash, Carol crossed the winning ...

two empty containers P and Q have the same volume. Water flows into P at the rate of 4 litres per minute and into Q at the rate of 6 litres per minute. After a certain time, container P can still take ...

The question was as follows-
on any given day, Andrea is equally likely to clock in at work any time from 8:50am to 9:06am. Similarly, Bert is equally likely to to clock in at work at any time from ...

Kate can mow the lawn in 45 minutes. Kate's sister takes twice as long to mow the same lawn. If they both have a mower and mow the lawn together, how many minutes will it take them?
I know the answer ...

First off I must say I'm pretty blown away by the vast majority of the people in this forum. I do aspire to reach the knowledge of mathematics as shown on the site, but honestly it's a little daunting ...

How do I prove that
$\cos^4A - \sin^4A+1=2\cos^2A$
$\cos^6A + \sin^6A =1-3\sin^2A\cdot\cos^2A$
I was going through a very old and very rich book of Plane Trigonometry to build a nice foundation for ...

Here's another problem, significantly harder than the first, but still accessible to target audience. The statement of the problem (i.e., northwest corner only) comes from a PennyDell puzzle magazine:
...

This is my first post. I hope it's acceptable.
EDIT Since there are people to whom such notation is foreign, I will point out that the problem represents KRRAEE / KMS, where PEI is the quotient and ...

While browsing on internet for different proofs of Fermat's theorem on sums of two squares, I came across Zagier's "one-sentence proof" which seems to be the most elegant and short proof. It invokes a ...

I came across the following problem on a UKMT senior maths challenege:
A hockey team consists of 1 goalkeeper, 4 defenders, 4 midfielders and 2 forwards. There are four substitutes: 1 goalkeeper, 1 ...

This is a very interesting word problem that I came across in an old textbook of mine. So I mused over this problem for a while and tried to look at the different ways to approach it but unfortunately ...

It is given that there are two sets of real numbers $A = \{a_1, a_2, ..., a_{100}\}$ and $B= \{b_1, b_2, ..., b_{50}\}.$ If there is a mapping $f$ from $A$ to $B$ such that every element in $B$ has an ...

What I know is that for equations of type $x+y=8$, $xy$ attains its maximum value when $x=y$ and this can be proved by either solving the quadratic equation with completing the squares or finding the ...

Are there any known methods to solve
$$2^x - 3^x + 6^x = 0,$$ where $x$ is either in closed form, perhaps in terms of special functions, or to give inequalities on the answers, where $x\in\mathbb{C}$ ...

In a game of 12 players that lasts for exactly 75 minutes there are 6 reserves who alternate
equally with starting players. It means that all players, including reserves, are in the game for
exactly ...

Let $n \in\mathbb{N}$ and $A=(a_{ij})$ where
\begin{equation}a_{ij}=\binom{i+j}{i}\end{equation}
for $0\leq i,j \leq n$. Show that $A$ has an inverse and that every element of $A^{-1}$ is an integer.
...

I have 3D grid of cells. Each cell can be in two states: visible, not visible. The camera is positioned on the side and looks at the grid. Random variable X is defined as a number of visible cells in ...